Oscillation- Hysteresis in Simple Triode Generators. 179 

 and grid potentials, namely 



^g=-J j Vay (1) 



where grid currents are assumed to be negligible. Thus in 

 such a case the variable part (« a ) of the anode current may 

 be expressed as a function of v a only, and it is precisely this 

 relation which is represented by the oscillation characteristic 

 mentioned above. In this way we are able to leave out of 

 account the retroactive action of the control electrode, and 

 deal simply with the problem of a conductor possessing a 

 characteristic relation i a =yfr(v a ) connected to an oscillatory 

 circuit, as shown in fig. 1 B. 



It will be seen that the problem we have to discuss is 

 exactly the same as that arising in the case of the dynatron 

 generator of A. W. Hull *, so that the general theory given 

 below Avill apply in toto to both triode and dynatron, if the 

 analogy between the oscillation characteristic of the former 

 and the direct characteristic of the latter is borne in mind. 

 We shall be concerned in general with the determination of 

 the possible stationary amplitudes, and also with the stability 

 of those amplitudes when the characteristic of either 

 generator is given. 



The application of KirchhofPs laws to such a circuit as is 

 shown in fig. 1 B leads to 



T di x Ty . If, , 

 ij-^=iit 2 + -^\i 2 dt= — v a , 



i 1 + i 2 =i a =ir(v a ), 



which together give 



2^ +Ri «) + stL c « +2 V} + cE= - • (2) 



But in the practical case of a high-frequency circuit, ~Ri a 

 is small compared with v a , and thus (2) may be written 



5 + |xH+^- = 0; .... (3) 

 where the subscripts of i a and v a have been omitted, uy has 

 been written for t^t ? an d x( v ) nas been written for 



We ha\e been unable to obtain a direct solution of (3), but 



* Hull. Proc. Inst. Radio En^. 6, i. Feb. 1918. 



N 2 



